ATLANTA, Jan 29 (Reuters) - Icy chaos gripped the U.S. South on Wednesday after a rare winter storm that killed at least six people, stranded children in their schools overnight and paralyzed travel in several states, including hundreds of flight cancellations at the world's busiest airport.

The storm slammed a region largely unaccustomed to ice and snow - stretching from Texas through Georgia and into the Carolinas on Tuesday and early Wednesday.

In Atlanta, motorists remained trapped in their cars on icy Interstates on Wednesday, some of them having spent as long as 18 hours on the road.

Some 791 traffic accidents were reported in the city but there were no serious injuries, Atlanta Mayor Kasim Reed said in a Wednesday news conference, adding that the focus was now on rescuing stranded motorists.

"We're going to get those people out of their cars," he said.

At least five deaths in Alabama and one in Georgia were blamed on the storm.

Airlines canceled thousands of flights at airports from Houston to Atlanta, with some 500 halted early Wednesday alone at the Hartsfield-Jackson Atlanta International Airport, the world's busiest.

"We are all in this together and we will get through it together," read a statement from police in Anniston, Alabama. "What was to be a simple dusting (of snow) has turned into something more. None of us were prepared."

Forecasters predicted little relief on Wednesday, with temperatures unlikely to rise much above freezing for long enough to thaw ice-covered roads and bridges, before dipping below freezing again early Thursday across the Southeast.

Precipitation was expected to ease later in the morning, and the wintry mix of snow, sleet and ice had moved farther to the East Coast on Wednesday from Georgia up through Maryland, where motorists were warned off the roads and schools were being closed or delayed.

TRAFFIC NIGHTMARES

A Facebook page called "Stranded Motorists Help Jan 28, 2014" which has 9,600 members, already had amassed entries from stranded motorists and volunteers trying to help them after an 18-hour gridlock continued to paralyze the Atlanta metro area.

Echo Garrett of Atlanta said a good friend of hers remained marooned on I-285 Wednesday.

"She's almost out of cell phone battery, no water, no food. No rescue vehicles," Garrett said in a message to Reuters.

Businesses and government in Atlanta, where 1 million people work, dismissed employees all at once early Tuesday afternoon, Reed said, causing the traffic crush.

"It hampered our ability to get our equipment on the ground," Reed said. "If there was one lesson learned in the middle of this challenge, that would be that we need to stagger closings from private sector companies, the government and the school system."

Atlanta school officials said on CNN that forecasts "drastically changed" after students had already been instructed to come to class.

In Birmingham, Alabama, authorities said a lack of warning about the severity of the ice led to thousands being stuck on roads, in shelters and in schools, with snow clearing vehicles having been initially directed south of the city where the ice was expected to hit.

"We proceeded to have school and have people go to their jobs," Mayor William Bell said. "When it came, it was too late."

The roads and Interstates there had begun to clear later Wednesday morning in Birmingham, with no injuries reported and no additional stranded motorists, police said.

Sections of major roadways remained closed in Louisiana near New Orleans, including the 24-mile Causeway Bridge spanning Lake Pontchartrain.

As the ice began to clear in Louisiana, some airlines resumed limited service Wednesday at Louis Armstrong New Orleans International Airport after about 24 hours of canceled flights.

Authorities rescued about 50 school children in Atlanta, whose buses were stranded overnight on an icy roadway, district officials said. Hundreds of other students remained sheltered in schools and other locations.

In Birmingham, about 800 students remained safe and fed in their schools early Wednesday, Bell said.

"We realize that is not good enough for parents who want to hold their children in their arms," Bell said. "We are doing all we can to reunite children with their parents." (Additional reporting by David Beasley in Atlanta, Verna Gates in Birmingham, Alabama; Kathy Finn in New Orleans; Harriet McLeod on Charleston, South Carolina; and Jon Herskovitz in Austin, Texas. Editing by Barbara Goldberg, Bernadette Baum and Gunna Dickson)